Epilepsy is a group of neurological disorders characterized by epileptic seizures, wherein electroencephalogram (EEG) is one of the most common technologies used to diagnose, monitor, and manage patients with epilepsy. A large number of EEGs have been recorded in clinical applications, which leads to visual inspection of huge volumes of EEG not routinely possible. Hence, automated detection of epileptic seizure has become a goal of many researchers for a long time. A novel method is therefore proposed to construct a patient-specific detector based on spatial-temporal complexity analysis, involving two commonly used entropy-based complexity analysis methods, which are permutation entropy (PE) and sample entropy (SE). The performance of spatial-temporal complexity method is evaluated on a shared dataset. Results suggest that the proposed epilepsy detectors achieve promising performance: the average sensitivities of PE and SE in 23 patients are 99% and 96.6%, respectively. Moreover, both methods can accurately recognize almost all the seizure-free EEG. The proposed method not only obtains a high accuracy rate but also meets the real-time requirements for its application on seizure detection, which suggests that the proposed method has the potential of detecting epileptic seizures in real time.